Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach

Harandi,Mehrtash T., Sanderson, Conrad, Hartley, Richard and Lovell, Brian C. (2012). Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach. In: Andrew Fitzgibbon, Svetlana Lazebnik, Pietro Perona, Yoichi Sato and Cordelia Schmid, Computer Vision – ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part II. 12th European Conference on Computer Vision, Florence, Italy, (216-229). 7-13 October, 2012. doi:10.1007/978-3-642-33709-3_16

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Author Harandi,Mehrtash T.
Sanderson, Conrad
Hartley, Richard
Lovell, Brian C.
Title of paper Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach
Conference name 12th European Conference on Computer Vision
Conference location Florence, Italy
Conference dates 7-13 October, 2012
Proceedings title Computer Vision – ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part II   Check publisher's open access policy
Journal name Lecture Notes in Computer Science   Check publisher's open access policy
Series Lecture Notes in Computer Science
Place of Publication Heidelberg, Germany
Publisher Springer
Publication Year 2012
Sub-type Fully published paper
DOI 10.1007/978-3-642-33709-3_16
Open Access Status
ISBN 9783642337086
9783642337093
ISSN 0302-9743
1611-3349
Editor Andrew Fitzgibbon
Svetlana Lazebnik
Pietro Perona
Yoichi Sato
Cordelia Schmid
Volume 7573
Issue Part 2
Start page 216
End page 229
Total pages 14
Collection year 2013
Language eng
Abstract/Summary Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of symmetric positive definite matrices, which form a Riemannian manifold. With the aid of the recently introduced Stein kernel (related to a symmetric version of Bregman matrix divergence), we propose to perform sparse coding by embedding Riemannian manifolds into reproducing kernel Hilbert spaces. This leads to a convex and kernel version of the Lasso problem, which can be solved efficiently. We furthermore propose an algorithm for learning a Riemannian dictionary (used for sparse coding), closely tied to the Stein kernel. Experiments on several classification tasks (face recognition, texture classification, person re-identification) show that the proposed sparse coding approach achieves notable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as tensor sparse coding, Riemannian locality preserving projection, and symmetry-driven accumulation of local features.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

 
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Created: Fri, 11 Jan 2013, 01:49:02 EST by Conrad Sanderson on behalf of School of Information Technol and Elec Engineering